Question 1                                                                                          

The Rutter Nursery Company packages its mulch in 50 kg bags. From a long history, the shipping department reports that the distribution of the bag masses follows the normal distribution and the standard deviation of this process is 3 kg per bag. At the end of each day, Jeff Rutter, the shipping manager, selects 10 bags and computes the mean mass of the sample. The sample mean was found to be 48.18 kg.

a)   Can Mr. Rutter conclude that the mean mass of the bags is less than 50 kg? Use the 1% significance level.                                                                                       

b)   Calculate the p-value.